Hello, because of the geometric sequence we can say that:
[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]
So there is no real root, so the function does not cut the x axis.
Thank you
For the given quadratic function, the x-axis is not cut by the function because there is no true root.
What is a quadratic function?To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.
As per provided data in question,
α = b/a = c/b
c/a = (c × b)/(a × b) = (c/b) (b/a) = α²
For the equation,
ax² + bx + c = 0
x² + b/a(x) + c/a = 0
⇒ x² + ax + α² =0
Δ = b² - 4 ac = α² - 4α²
Δ = -3α² < 0, which means that no real root is there.
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intercept is the length from origin to intersection point of respective axis,
it intersects x axis at -7.5 and y is 0 so x intercept is (-7.5,0)
and similarly, y intercept is (0,5.5)
Answer:
(- 7.5, 0 ) and (0, 5.5 )
Step-by-step explanation:
The x- intercept is the value of x on the x- axis where the line crosses.
Here the line crosses the x- axis at - 7.5 , thus the coordinates of x- intercept
(- 7.5, 0 )
The y- intercept is the value of y on the y- axis where the line crosses.
Here the line crosses the y- axis at 5.5 thus the coordinates of the y- intercept
(0, 5.5 )
if a man works 400km in 6 minutes.How long will he work in 9 minutes
Answer:
600 kmStep-by-step explanation:
400 km = x
6 min 9 min
cross multiply:
6x = 400 ( 9)
x = 3600 / 6
x = 600 km
Help a friend out I don’t understand it
Answer:
THEY ARE COMPLIMENTARY BUT NOT NECESSARILY CONGRUENT.
Step-by-step explanation:
This is so because their lines don't meet.
243 as a power of 3
Answer:
243 as a power of 3
= 3^5
=243
Each serving of a pancake recipe calls for 1/4 cup of flour. How many servings can be made with 2 cups of flour?
Answer:
The correct answer is 8 servings of pancakes.
Step-by-step explanation:
If each serving of pancakes calls for 1/4 cup of flour, to find how many servings can be made with 2 cups of flour, we should divide 2 cups by 1/4 cup.
To do this, we can first convert 1/4 to a decimal by dividing the numerator by the denominator.
1/4 = 0.25
Next, we can go ahead with the division.
2 / 0.25 = 8
Therefore, 8 servings of pancakes can be made with 2 cups of flour.
Hope this helps!
The fraction subtracted from 5/3 to get 1 is_____
Answer:
2/3
Step-by-step explanation:
I am not sure
Answer:
2/3Step-by-step explanation:
[tex]Let \:the \: unknown \: fraction \: be \: x\\\\\frac{5}{3} -x = 1\\\\\frac{5}{3}-x=1\\\\\mathrm{Subtract\:}\frac{5}{3}\mathrm{\:from\:both\:sides}\\\\\frac{5}{3}-x-\frac{5}{3}=1-\frac{5}{3}\\\\\frac{5}{3}-x-\frac{5}{3}=-x\\\\1-\frac{5}{3}=-\frac{2}{3}\\-x=-\frac{2}{3}\\\\x=\frac{2}{3}\\[/tex]
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hour is desired. Past studies suggest that a population standard deviation of hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Complete question:
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:
111 students
Step-by-step explanation:
Given the following :
Margin of Error (E) = 0.28
Population standard deviation (sd) = 1.5
Recall:
Margin of Error(E) = Z * (sd/√n)
Taking a confidence interval of 95%
The Z value at a 95% confidence interval is 1.96
Plugging our values, we have :
Margin of Error(E) = Z * (sd/√n)
0.28 = 1.96 * (1.5/√n)
0.28 = 2.94 / √n
√n × 0.28 = 2.94
√n = 2.94 / 0.28
√n = 10.5
Square both sides to obtain n
n = 10.5^2
n = 110.25
What's the correct answer to this..? Need help
Answer:
A.
Step-by-step explanation:
All of those graphs represent functions. You are able to tell because they all pass the vertical line test. The vertical line test is conducted by drawing a line that goes vertically and intercepts any point of the line in question. If the function crosses the vertical line twice, it is not a function. If it only intercepts once, it is a function. In this case, every graph is a function because they would intercept a vertical line once.
A small toy car costs $3. A large toy car costs 5 times as much as the small one. Aaron wants to buy one of each. Which equation can he use to find the cost (a) of the two cars?
Answer: He can use 3 x 5 = 15 and 15 + 3.
Step-by-step explanation:
Since a small car is $3, and the large car is 5x the price of the small car, he can use the equation 3 x 5 = 15, because the small car is $3, and the large car is 5x the price. You can use 15 + 3 = 18, because the small car is $3, so you also have to add that.
Here to help!
The equation is x + 5x = 18 , where x is the cost of small toy car and the total cost of the two cars = $ 18
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost of the two cars be A
Now , the equation will be
Let the cost of the small toy car be = x
The cost of small toy car = $ 3
The cost of the large car = 5 x cost of small toy car
Substituting the values in the equation , we get
The cost of the large car = 5 x 3
The cost of the large car = $ 15
So , the cost of two cars = x + 5x
Substituting the values in the equation , we get
The total cost of the two cars A = 15 + 3
The total cost of the two cars A = $ 18
Therefore , the value of A is $ 18
Hence , the equation is A = x + 5x
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what is the lcm of 7÷25 and 3÷25
Answer:
LCM of 7/25 and 3/25 is 25
Step-by-step explanation:
The full meaning of LCM is Lowest (Least) Common Multiple
Lowest (Least)Common Multiple can be defined as the lowest or least number that is the multiple of two or more number. Note that this least number is not zero
Lowest(Least) common Multiple when applied to fractions is the least number that is the multiple of the denominators of the fraction.
In the above question, we are asked stop find the LCM of 7÷25 and 3÷25
= LCM of 7/25 and 3/25
The two denominators are the same, hence, the LCM is 25.
Tony knew there was a solution to his math problem in one of four textbooks. He got some information from his classmates about it: Andy: "The solution is in either book 1 or 2"; Billy: "The solution is in either book 3 or 4"; Charlie: "The solution is in book 4"; Danny: "There is no solution in book 3". Emily helped Tony by saying that only one of his classmates was right, and the other three were mistaken. Which book has the solution in it?
Answer:
Charlie is the right person.
Step-by-step explanation:
The right person is Charlie because he was sure of what he was saying. Others were not sure making them mention two textbooks while Danny didn't answer the question Tony asked because he was talking about the one that doesn't have the solution.
commom difference of an AP -4 , -4 , -4 ,............is...
Answer:
0
Step-by-step explanation:
Common Difference = Difference between any two consecutive terms
= - 4 - (-4)
= - 4 + 4
= 0
You move at 45/mph and a bullet is shot at you, the bullet is moving at 44/mph
Would you be able to dodge the bullet, you factor in the fight or flight or freeze response
Answer:
See explanation below.
Step-by-step explanation:
A bullet shot at you will definitely hit you because of the direction it is travelling.
Your fight and flight response won't be activated either because of the speed of the event (bullet) or if you don't know how harmful a gun is (you'll remain calm/ignorant in this case)?
Try to post academic problems.
Best Regards!
Solve for u.
– 22 = -8u + 6(u-7)
Simplify your answer as much as possible.
Step-by-step explanation:
- 22 = -8u + 6(u-7)
-22 = -8u + 6u - 42
8u - 6u = 22 - 42
2u = -20
u = -20/2
u = -10
Answer:
[tex] \boxed{ \boxed{ \mathrm{ \bold{ \blue{ - 10}}}}}[/tex]Step-by-step explanation:
[tex] \mathrm{ - 22 = - 8u + 6(u - 7)}[/tex]
Distribute 6 through the parentheses
⇒[tex] \mathsf{ - 22 = -8u + 6u - 42}[/tex]
Collect like terms
⇒[tex] \mathrm{ - 22 = - 2u - 42}[/tex]
Swap the sides of the equation
⇒[tex] \mathrm{ -2u - 42 = - 22}[/tex]
Move constant to R.H.S and change it's sign
⇒[tex] \mathrm{ - 2u = - 22 + 42}[/tex]
Calculate
⇒[tex] \mathrm{ - 2u = 20}[/tex]
Divide both sides of the equation by -2
⇒[tex] \mathrm{ \frac{ - 2u}{ - 2} = \frac{20}{ - 2} }[/tex]
Calculate
⇒[tex] \mathrm{u = - 10}[/tex]
Hope I helped!
Best regards!
Do the ratios 2/3 and 12/18 form a proportion?
yes
no
Answer:
Yes
Step-by-step explanation:
Because 12/18 = 2/3..(cancel 12 and 18 by 6)
Answer:
yes
Step-by-step explanation:
2x6=12
3x6=18
6 is the multiplying number
( the 2 equations are the same amount )
standard form of 6,32,94,000
Answer:
6.3294✖️10^7
Step-by-step explanation:
To find the statdard form, you place the decimal after the largest unit, int his case 6.
Then you write down all the numbers except for "0".
This becomes:
6.3294
Then, you add the multiplying sign, and count how many digits are there after 6, and in this case, there are 7, so you add the power "7" after 10.
6.3294✖️10^7
Hope this helped!
Have a nice day:)
what is the square root of 450
Answer:
[tex]15\sqrt{2}[/tex] or 21.2132
Step-by-step explanation:
[tex]\sqrt{450}[/tex]
[tex]\sqrt{15^{2} }[/tex] (root of a product is equal to the product of the roots of each factor)
[tex]\sqrt{15^{2} } \sqrt{2}[/tex] (simplify)
[tex]15\sqrt{2}[/tex] or ≈ 21.2132
Answer:
[tex]15\sqrt{2}[/tex] or 21.213
Step-by-step explanation:
For radical form: think of multiples of 450. Think of a pair that contains one perfect square, particularly the higher, the better . These 2 numbers are 25 and 18. 25 is the perfect square number since the two numbers that multiply to be 25 is 5 and 5.
Now take the perfect square of 25 and put it outside of the radical. The 18 remains inside: [tex]5\sqrt{18}[/tex]
Now, since 18 is a high number that needs to get reduced, do the same for 18 as we did for 450--find two numbers, one of which is a perfect square. These two numbers are 9 and 2.
Now take the perfect square of 9. This is 3. Take it out of the radical so that only the two remains inside. The 3 will now multiply with the 5: [tex]5*3\sqrt{2}[/tex]
Multiply 5 and 3 to get 15. The 15 stays outside the radical. Your answer is:
[tex]15\sqrt{2}[/tex]
the work in an office takes 180 hours to complete every work
each person in the office works for 35 hours a week
what is the smallest number of people needed to complete the work?
Answer:
Minimum People required = 5
Step-by-step explanation:
Total hours required to complete the work every week = 150 hrs.
Number of hours worked per week by one person = 32 hr
∴ Number of people required to complete the work per week = Total number of hrs to complete the work ÷ No of hrs work per person
∴ Number of people = 150 ÷ 32
∴ Number of people = 4.6875
This is the minimum number of people. But no of people cannot be a fraction.
Thus, rounding the number to next integer.
∴ Smallest number of people needed to complete the work = 5
A radioactive substance decays exponentially. A scientist begins with 350 milligrams of a radioactive substance. After 14 hours, 175 mg of the substance remains. How many milligrams will remain after 20 hours
Answer:
N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg
therefore, N(t)=130∗.545/24=35.44mg
Step-by-step explanation:
N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg
therefore, N(t)=130∗.545/24=35.44mg
Answer:
≈ 130 mg
Step-by-step explanation:
This is about the half-life of the substance.
There is a formula for this kind of calculations:
N(t)= N₀*(0.5)^(t/T), where
N(t) = substance left after time period of t,t = time passed,N₀ = initial amount of the substance,T = hal-life time of the given substance.In our case, we have:
N₀ = 350 mg,t= 20 hours,T = 14 hours as half of substance decays during this time period,And the calculation:
N(20)= 350*(0.5)^(20/14)N(20) ≈ 130 mgAnswer: about 130 mg of substance remains after 20 hours
How do you graph y=2/3x-4
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▹ Answer
You can use a graphing calculator.
▹ Step-by-Step Explanation
Attached is a screenshot.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
See explanation and picture attached
Step-by-step explanation:
We can break down this expression into it's core components:
Since the constant here is -4, the y intercept is -4.
Since the value we are multiplying x by is [tex]\frac{2}{3}[/tex], the slope is [tex]\frac{2}{3}[/tex]. This means for every time we go horizontal 3 units, the line increases by 2.
The graph is attached.
Hope this helped!
which one is irrational?
Basically everything but choice C
==========================================
Explanation:
sqrt is shorthand for square root
sqrt(4) = 2 = 2/1 showing that sqrt(4) is rational. We can write it as a fraction of two whole numbers, where 0 is not in the denominator.
-------
In contrast, we cannot write sqrt(2), sqrt(3), or sqrt(5) as a fraction of two whole numbers. Using your calculator, note how
sqrt(2) = 1.4142135623731
sqrt(3) = 1.73205080756888
sqrt(5) = 2.23606797749979
all of those decimal expansions go on forever without any pattern, which is a sign that those numbers are irrational. If they were rational, then a pattern would repeat at some point or the decimals would terminate at some point.
Answer:
a, b, d are irrational
Step-by-step explanation:
root 2 = 0.414.....
root 3 = 0.732.....
root 5 = 2.236.....
Hope this helps.....
Pls mark my ans as brainliest
If u mark my ans as brainliest u will get 3 extra points
Please help ! First one to give correct answer gets brainliest!
Answer:
(4x+1)²
Step-by-step explanation:
Which geometric figure has 120 rotational symmetry?
Answer:
Triangle
Step-by-step explanation:
Has 120° degrees of rotation and measure of the central angle and has 3-fold rotational symmetry
The family size bottle of sunscreen holds 12121212 fluid ounces (fl oz)(\text{fl oz})(fl oz)(, start text, f, l, space, o, z, end text, )of sunscreen. The regular bottle holds 75%75\%75%75, percent less.How many fewer fluid ounces does the regular bottle of sunscreen hold?
Answer:
The regular bottle holds 9 fl oz less
Step-by-step explanation:
Given
Family Size = 12 fl oz
Required
Determine the size held less by the regular bottle
From the question, we have that the regular bottle holds 75% less;
[tex]Regular\ Size = 75\% * Family\ Size[/tex]
Substitute 12 fl oz for Family Size
[tex]Regular\ Size =75\% * 12\ fl\ oz[/tex]
Convert percentage to fraction
[tex]Regular\ Size = \frac{75}{100} * 12\ fl \oz[/tex]
[tex]Regular\ Size = \frac{75 * 12\ fl\ oz}{100}[/tex]
[tex]Regular\ Size = \frac{900\ fl\ oz}{100}[/tex]
[tex]Regular\ Size = 9\ fl\ oz[/tex]
Hence, the regular bottle holds 9 fl oz less
On a coordinate plane, triangle A B C is shown. Point A is at (negative 2, negative 4), point B is at (2, negative 1), and point C is at (3, negative 4). Triangle ABC is an isosceles triangle in which side AB = AC. What is the perimeter of triangle ABC? 5 + StartRoot 10 EndRoot units 10 + StartRoot 10 EndRoot units 10 StartRoot 10 EndRoot units 50 units
Answer:
B, 10+ /10 units
Step-by-step explanation:
The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
Answer:
2,041 square centimeters
Step-by-step explanation:
surface area = (2 × π × r × h) + ((π × r) × (r+ (√(c² + r²))))+(π × r²)
where,
cylinder base radius (r) = 10 cm
height of cylinder (h) = 16 cm
total height = 28 cm
cone height (c) = total height - height of cylinder = 28 - 16 = 12cm
π = 3.14
surface area = (2 × 3.14 × 10 × 16) + ((3.14 × 10) × (10+ (√(12² + 10²))))+(3.14 × 10²)
surface area = 1004.8 + (31.4 * 25.6) + 314
surface area = 2122.64 cm²
therefore the approximate surface area given is 2,041 square centimeters
Donny has three times as many candy canes as Marc. Marc has thirty more candy canes than Bob. They have 500 candy canes altogether. How many candy canes does Donny have?
Answer:
318
Step-by-step explanation:
Bob=x
Marc=x+30
Donny=3(x+30)
x+x+30+3x+90=500
5x=500-120
5x=380
x=76
Bob has x = 76
Marc has x+30=106
Donny has 3*112=318
318+106+76=500
Write an expression that can be used to find the price of a television that is on sale for 20% off the regular price of p dollars. Can you write a second expression equivalent to the one you wrote in the last questions.
Answer:
The expression that could help calculate the price of the TV is;
$P - 20% of $P
Step-by-step explanation:
Here, we want to write an expression that corresponds to the price of a television set that is on sale at a price which is 20% off the regular price.
From the question, we can see that the regular price is $P
So now we are having 20% off;
This corresponds to;
20/100 * p = p/5 = 0.2p
So in the expression form, we can have;
$P - 20% of $P
A set of furniture was sold for GH cedis 3000 at a profit of 25%. Find the cost price.
Answer:
2400GH CedisStep-by-step explanation:
[tex]Selling \:price = 3000gh Cedis\\Profit \% = 25\%\\Cost\:price =?\\\\CP =\frac{ ( Selling\:price \times 100 )}{ ( 100 + percentage profit)} \\\\C.P = \frac{3000\times 100 }{100+25}\\\\ C.P = \frac{300000}{125} \\\\Cost\: Price = 2400gh Cedis[/tex]
A line passes through point (4,-3) and has a slope of 5/4. Write an equation in Ax + By = C
Answer:
The answer is
5x - 4y = 32Step-by-step explanation:
To write an equation of a line using a point and slope use the formula
y - y1 = m(x - x1)where
m is the slope
(x1 , y1) is the point
So we have
Equation of the line using point (4 , -3) and slope 5/4 is
[tex]y + 3 = \frac{5}{4} (x - 4)[/tex]
Multiply through by 4
4y + 12 = 5(x - 4)
4y + 12 = 5x - 20
5x - 4y = 20 + 12
The final answer is
5x - 4y = 32Hope this helps you
